A reformulation of the LUC CNDO approach to the properties of solids. I. General theory

Abstract

Hartree-Fock equations are solved for a large unit cell (LUC) periodic system using the linear combination of atomic orbitals (LCAO) approach and within the k=0 semiempirical complete neglect of differential overlap (CNDO) approximation. Convergence difficulties in previous approaches are resolved by careful analysis of the density matrix dependent terms in the Fock matrix. Detailed studies of the density matrices of analytically solvable one-dimensional tight-binding models give insight into the properties of distance-dependent modulating functions that weight certain Coulomb interaction terms. It is shown that the k=0 approximation cannot be fully self-consistent, but it is nevertheless possible to develop satisfactory total energy algorithms that converge rapidly with interaction distance.